Qiuyu Ren

I am a third year PhD student in pure mathematics at UC Berkeley working with Ian Agol. My research interests include low-dimensional topology (mostly 4-manifolds and knot theory) and some symplectic geometry.

Here is my cv (03/22/2024).

Ongoing/Upcoming Events

• Coorganizing the student 3-manifold seminar at UC Berkeley with Ethan Dlugie.
• Will participate in the 2024 Georgia topology summer school and conference, May 2024.
• Will participate in the conference Combinatorial and Gauge theoretical methods in low dimensional topology and geometry at the Centro di Ricerca Matematica Ennio De Giorgi in Pisa, Italy, June 2024.
• Will give a talk in the Research Seminar on Quantum Topology and Categorification (QTCat) at the University of Hamburg, Germany, June 12nd, 2024.
• Will give a talk in the Knot Online Seminar (K-OS), June 13rd, 2024.
• Will participate in the Summer school in Mathematics: Low dimensional topology at Grenoble, France, June 2024.
• Will visit the University of Zurich, Switzerland, August 2024.
• Will give a talk in the AMS 2024 Fall Central Sectional Meeting, University of Texas, San Antonio, September 2024.

Publications/Preprints/Expositories

• Khovanov homology and exotic $4$-manifolds, with Michael Willis
• Toroidal Hitomezashi Patterns, with Shengtong Zhang
• Slice genus bound in $DTS^2$ from $s$-invariant, to appear in Algebraic and Geometric Topology
• Lee filtration structure of torus links, to appear in Geometry and Topology
• A succinct proof of Defant and Kravitz’s Theorem on the length of Hitomezashi loops, with Shengtong Zhang, Annals of Combinatorics (2024)
• Spectral asymptotics for kinetic Brownian motion on Riemannian manifolds, with Zhongkai Tao
• Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces, with Zhongkai Tao

Below are some purely expository papers. Read with caution.
Toric Varieties in Algebraic and Symplectic Geometry (final paper for MATH 256A, UCB Fall 2021)
Equivariant de Rham Theory (notes for an independent reading course, MIT Spring 2020)
Linear Fractional Transformations on the Berkovich Projective Line (final paper for an independent study course in p-adic analysis, MIT Spring 2019)
Spectral Properties of the Laplacian on Compact Lie Groups (one of the projects for 18.821, MIT Fall 2020; see the end to see my part of writing)
Conjugacy of Cartan Subalgebras (final paper for 18.745, MIT Fall 2019)
Complex Analytic Proofs of Bernstein's Theorem (final paper for 18.994, MIT Spring 2020; I wrote Section 4 and 6)
Points of Continuity of Real Functions on the Real Line (random thing asked by a friend)

Past Events

• Gave a talk in the University of South Florida geometry and topology seminar, April 2024.
• Gave a talk in the Simons Collaboration satellite conference: Floer homology, low-dimensional topology, and algebra, Princeton University, March 2024.
• Gave a talk in the UC Davis geometry and topology seminar, March 2024.
• Participated in the 2024 Geometry and Topology Workshop at UCLA, January 2024.
• Participated in the Workshop on exotic 4-manifolds at Stanford University, December 2023.
• Gave a talk in the Texas A&M topology seminar, October 2023.
• Gave a talk in the Caltech geometry and topology seminar, September 2023.
• Gave a talk in the Stanford topology seminar, September 2023.
• Gave a talk in the MIT geometry and topology seminar, September 2023.
• Participated in the conference Gauge Theory and Topology: in Celebration of Peter Kronheimer’s 60th Birthday at the Clay Mathematics institute in Oxford, July 2022.
• Visited Instituto de Ciencias Matemáticas (ICMAT) in Madrid for the conference Geometric group theory and low-dimensional geometry and topology, June-July 2022.
• Participated in the Analytic and Geometric Aspects of Gauge Theory and Floer Homotopy Theory programs at MSRI/SLMath, Fall 2022.
• Coorganized a reading group on the Kobayashi-Hitchin correspondence with Yueqing Feng, Fall 2022.
• Organized a reading group on Donaldson & Kronheimer's The Geometry of Four-Manifolds, Summer 2021. I am also maintaining an errata list for the book.
• University of Chicago Research Experience for Undergraduates (REU), Summer 2020, resulted in a summary paper on Kähler quantization commuting with symplectic reduction.
• MIT Undergraduate Research Oppotunities Program (UROP), Spring 2020, with Zhuofan Xie under the guidance of Professor Paul Seidel, resulted in a paper on nonnegatively curved sl(2,R)-connections on surfaces.
• MIT Summer Program in Undergraduate Research (SPUR), Summer 2019, mentored by Yuqiu Fu on a problem proposed by Professor Larry Guth related to the Kakeya conjecture. My paper won the Hartley Rogers Jr. Prize.

Others

If you're looking to pass the time and can read Chinese, here are some fun logic puzzles.